bis 1.492

This section presents a description of model estimation results. Many alternative model specifications were tested to arrive at the final model specification. It should be noted that a number of potential explanatory variables were not included in the residential location (density) choice utilities because of potential endogeneity effects. Variables such as dwelling unit type, vehicle ownership, and number of drivers may be regarded as endogenous to residential location choice and were hence omitted from the specification.

However, a number of such variables are included in the household VMT regression equation. Also, to avoid an entanglement of built environment attributes embedded in the residential choice definition with any other built environment attributes that could be introduced separately in the household VMT regression equation, no additional built environment attributes are introduced in the VMT equation.

Repeated attempts were made to estimate a full model specification with spatial dependency. A variety of spatial dependency forms were specified and used to define the weight matrices that represent strength of association between observations. Every specification that was attempted yielded a spatial dependency or autoregressive parameter ( ) that was not statistically significantly different from zero. Reasons for the statistical insignificance of the spatial dependency parameter are not immediately clear, but the fact that the parameter repeatedly showed up insignificant for a large variety of specifications suggests that the spatial dependency effects may truly be insignificant in this particular data set, or there are other unknown forces at play that are rendering this effect to be existent. Due to the insignificance of the spatial dependency effect, only the final non-spatial or anon-spatial model estimation results are presented. In addition, the allocation of household VMT to various contributing factors omits spatial dependency effects and only considers the three other effects (socio-economic and demographic, residential self-selection, and built environment) together with unexplained or unknown effects.

Model estimation results for the aspatial model with self-selection are shown in Table 2. An independent model that ignores self-selection effects engendered through error covariances was also estimated; results for that model are quite similar to those seen in the

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model with self-selection and hence the table of results for the independent model system is omitted. The residential location (density) model component takes the form of a multinomial probit (MNP) model while the vehicle miles of travel model component takes the form of a continuous log-linear regression model.

In the MNP model of residential location (density) choice, it can be seen that alternative specific constants for the medium and high density categories are negative, suggesting that ceteris paribus, households are more likely to locate in low density neighborhoods. Single persons are more likely, however, to locate in high density neighborhoods. Consistent with descriptive statistics seen earlier and prior research (Cao and Fan, 2012), lower income households are more likely to locate in medium- and higher density neighborhoods, as are households belonging to ethnic minority segments (African-American and Hispanic). Households with a higher fraction of unemployed individuals are less likely to locate in high density neighborhoods, presumably because households in low density neighborhoods are of larger household size with children (who are naturally unemployed).

In the continuous linear regression model, the fraction of individuals in the household in the middle age groups is positively associated with household VMT production, presumably because such households are at a lifecycle stage that is associated with a high level of trip-making, compared to households with a higher fraction of individuals in older age groups (Collia et al, 2003). Residential location (density) is found to significantly affect household VMT, consistent with the pattern seen in Figure 1 and as reported extensively in the literature. Households in medium and high density neighborhoods produce fewer VMT as evidenced by the negative coefficients, with the effect amplified in the context of high density areas relative to medium density areas. As expected, vehicle ownership is a strong predictor of household VMT with multi-vehicle owning households likely to generate more VMT than other vehicle ownership groups.

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Table 2. Joint Residential Location (Density) and Aspatial Household VMT Model with Self-Selection

Variables

MNP Residential Choice Continuous LR

Low Density Coef (t-stat)

(base)

Medium Density Coef (t-stat)

High Density Coef (t-stat)

Natural Log of vehicle miles traveled Coef (t-stat)

Constant - -0.1233 (-4.23) -0.1929 (-5.37) 0.8429 (8.4)

Family structure Variables

Single Person - - 0.1839 (3.62) -

Couple - - - -

Nuclear Family - - - -

Joint Family - - - -

Household Income Variables [US$/year]

Below 30,000 - 0.2145 (3.15) 0.2069 (2.83) -

30,000 to 75,000 - - - -

75,000 to 150,000 - - - -

Household race and ethnicity

African-American - 0.3342 (3.96) 0.4100 (4.84) -

Hispanic - 0.4533 (4.14) 0.6362 (5.85) -

Other races - - - -

Fractions of household in age-groups

Age 16 to 35 - - 0.1701 (2.01) -

Age 35 to 55 - - - 0.2330 (3.13)

Age 55 to 65 - - - 0.2013 (2.73)

Age above 65 - - - -

Residential Density

Medium density - - - -0.4309 (-7.52)

High density - - - -0.7619 (-13.28)

Number of vehicle in household

One vehicle - - - 1.6606 (22.35)

Two or more vehicles - - - 2.5955 (32.45)

Number of workers in household - - - 0.1505 (4.70)

Number of students in household - - - 0.1388 (2.55)

Fraction of unemployed in household - - -0.3073 (-3.54) -

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A review of error variance-covariance estimates in the matrix Λ

for the independent model system (where error covariances across the discrete choice and linear regression model components are restricted to zero; that is, all elements of the matrix Ψ are set to zero) and the joint model system (that accounts for self-selection effects through the elements of the Ψ matrix) reveals a statistically significant covariance between density categories in the residential location choice model. In particular, referring to Equation (13), the estimated value of ₂₃ is 0.4437 (t-statistic of 8.12), and that of ₃² is 1.002 (t-statistic of 9.60) in the joint system (these estimated values were similar in the indpendent model).

The positive value of ₂₃ suggests that unobserved attributes that contribute to living in a medium (high) density configuration positively contribute to residing in a high (medium) density area (though, very technically, the matrix Λ

is a differenced utility matrix with respect to the low density category). This result is consistent with expectations. Attitudes and lifestyle preferences that motivate an individual to seek residential locations in higher density areas are likely to positively influence choice of residence in both medium and high density neighborhoods.

In the model with self-selection, it is found that significant error covariances exist between residing in medium or high density neighborhoods (relative to low density living) and vehicle miles of travel. Specifically, the estimated values of _2 and _3 are 0.108 (t-statistic of 2.19) and 0.089 (t-(t-statistic of 1.92), respectively. These significant error covariances demonstrate the importance of modeling these choices (i.e., residential location and household VMT) jointly in a simultaneous equations modeling framework capable of accounting for shared unobserved attributes affecting multiple endogenous variables of interest. What is interesting is that both error covariances are positive and significant. In other words, unobserved attributes that contribute to residing in higher density neighborhoods (relative to residing in low density neighborhoods) also contribute to an increase in household VMT after accounting for observed exogenous covariates included in the model specification. Although this may appear counter-intuitive at first glance, it is not necessarily so. The very unobserved attributes that contribute to seeking

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residential location in higher density neighborhoods may very well contribute to higher VMT production. After controlling for built environment attributes and household socio-economic and demographic characteristics, households that favor active lifestyles and seek a variety of activity opportunities (latent unobserved traits) are likely to undertake more travel and hence produce more VMT than observationally equivalent households that have different (more sedentary) lifestyle preferences.

An examination of goodness-of-fit statistics reveals that the composite log-likelihood value for the joint model with 25 parameters is -10,233.30 while the corresponding value for the independent model (with 23 parameters) is -10,236.39. The goodness-of-fit of the two models may be compared using the adjusted composite

2 distributed (Bhat, 2011).

2 table value with two degrees of freedom at a 95 percent confidence level. This shows that the model with self-selection offers a statistically significant, but not necessarily very large, improvement in fit to the data.

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